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      All ASD complex and real 4-dimensional Einstein spaces with \(\Lambda \ne 0\) admitting a nonnull Killing vector

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          Abstract

          Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant \(\Lambda\) equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Pleba\'nski equation (Toda field equation). Some alternative form of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex spaces admitting a nonnull Killing vector are found.

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          Author and article information

          Journal
          1312.4284
          10.1142/S0219887816500110

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Mathematical physics, Mathematical & Computational physics

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